Events in MathSys and Complexity Science
This is a calendar page detailing events within the MathSys CDT. It also acts as a booking diary for the Seminar Room D1.07. To book D1.07 please email Sheetal.Sharma@warwick.ac.uk
Please note that your event booking is for D1.07 only. The adjacent common room is a private area for the MathSys Centre that cannot used as part of your booking.
MathSys CDT events have priority for D1.07 room bookings.
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Mark Ancliff: Solution of quasispecies models using spin coherent states
Abstract
Quasispecies models describe the evolution of an asexually reproducing population subject to random mutation and selection. Individuals are labelled by a DNA-like string of letters of a fixed length N, and the population is described by a distribution function on the set of possible strings. Quasispecies models are a popular starting point for theoretical studies of molecular evolution, and have recently been applied to studies of virus-immune system interactions, evolution in changing environments, and extended to include sexual reproduction.
Two of the most commonly studied quasispecies models can be mapped onto a quantum spin system similar to the one-dimensional quantum Ising model, which allows the application of several techniques from statistical physics.
Here I present a new method for calculating the dynamics and equilibrium population distribution in these quasispecies models by constructing a spin coherent-state path integral representation of the evolution operator. In the large N limit a semi-classical approximation gives a description in terms of a classical Hamiltonian function on a sphere. Using this method I will present several new results relevant to biological systems including evolution of the mutation rate, adaptation in changing environments, and a model of escape from adaptive conflict.